Remarks on the rings of functions which have a finite numb er of di scontinuities
| Autor: | Mohammad Reza Ahmadi Zand, Zahra Khosravi |
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| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Applied General Topology, Vol 22, Iss 1, Pp 139-147 (2021) |
| Druh dokumentu: | article |
| ISSN: | 1576-9402 1989-4147 |
| DOI: | 10.4995/agt.2021.14332 |
| Popis: | Let X be an arbitrary topological space. F(X) denotes the set of all real-valued functions on X and C(X)F denotes the set of all f ∈ F(X) such that f is discontinuous at most on a finite set. It is proved that if r is a positive real number, then for any f ∈ C(X)F which is not a unit of C(X)F there exists g ∈ C(X)F such that g ≠ 1 and f = gr f. We show that every member of C(X)F is continuous on a dense open subset of X if and only if every non-isolated point of X is nowhere dense. It is shown that C(X)F is an Artinian ring if and only if the space X is finite. We also provide examples to illustrate the results presented herein. |
| Databáze: | Directory of Open Access Journals |
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